Step control

Step Control

For the fixed step tracing methods Ichnos provides 4 parameters to control the step.

Step size

The step size sets the length of the step. The next point is calculated as

Pnew = Pold + norm(V)*step

where Pold and Pnew is the current and the next position of the particle norm(V) is the normalized velocity and step is the step size.

N Steps

The idea for this is to have a control to define how many steps to take inside an element. However, in the case of CLOUD type there are no elements involved. The elements can be approximated by using the parameters diameter and ratio. Using the parameters from the point closest to the current particle position the code creates a bounding box. Then calculates the length of the line segment that is bounded by the bounding box and pass through the particle position along the direction of velocity. The step size is set equal to the length/nSteps.

Step Size Time

Instead of specifying the length of the step it may be desirable to control the time. Let's suppose that the Step size was set 50 m. Then depending on the velocity the particle could traverse those 50 m either fast of very slow. With that parameter one can define the maximum time. Then the actual step with length units is recomputed as:

step = length(V)*StepSizeTime

N Steps Time

This is a way to define how many steps the particle tracking has to take within the current time step. This is ignored in steady state velocity fields. After the code has identified which is the current time step divides the time span by this parameter and the converts the step to length as previously.

minExitStepSize

When the algorithm takes a step that the next point is outside the domain the code discards the new point reduces the step to 45% of the initial step and performs another step. This is repeated until the step size is less than the minimum exit step size.

Guidelines

One can set all of those parameters. The final step will be the smallest of all 4. It is possible to set just one or two of them. The StepSize is the easiest and most predictable control. The streamline will consist of equally spaced points. The Nsteps is very useful in simulations where the element sizes and therefore the density of points vary in space. If there are regions where the density of points is higher than the fixed step size then the Nsteps will make sure that the particle tracking will not jump the small elements. The StepSizeTime is the most unpredictable because it depends on the velocity of the field. As such it's should be used in conjunction with the other controls. Finally, the StepSizeTime provides a good control for transient simulations. However, because the groundwater flow fields are generally very slow this will result streamlines with many thousands of points, big output files and longer simulation times.